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The Problem With Robo-Advisors’ Use of Mean Variance Optimization

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If you read the industry press, you can’t avoid the topic of robo advisors. Will they replace human advisors? If you can’t beat ‘em, should you join ‘em? How can a robo platform complement your practice? There are many questions and countless articles. While those questions are important to the overall conversation, one issue that hasn’t been widely addressed is the theoretical underpinnings. I’d like to address the topic – basically take a look “under the hood.” 

At their core, robos are based on mean-variance optimization (MVO) the key to which is a portfolio variance formula that works like this in a two-asset example: 

Portfolio Variance = [WEIGHT SQUARED OF ASSET 1] * [VARIANCE OF ASSET 1] +



Since standard deviation is simply the square root of variance, all we really have are weights, variances and correlations.

There are three components of this formula – the first and second are the product of the asset’s squared weight and its variance and the third line is the product of the correlation between the assets and square roots of their variance. MVO is simply an algorithm that selects a set of weights for assets 1 and 2 such that the overall portfolio variance is as low as possible for a given return requirement. This technique has been widely used since the 1980s by large fund managers, including hedge funds.

While MVO is an important financial tool, let loose on individual investors it can be a disaster waiting to happen.

Why Optimizers Can Be “Error Maximizers”

Sophisticated traders (such as hedge funds and large asset managers) use MVO, but they always take great care to constrain the optimizer, because without constraints the optimizer would produce crazy portfolios. In fact, it’s often said that optimizers are error maximizers. Here’s why: The optimizer works with parameters that are not certain. We don’t know ‘true’ variance of any security; we don’t know its ‘true’ correlation with other securities; and we certainly don’t know the future return on those securities. So we work with estimates of those parameters.

Despite its computational power, an optimizer is essentially a dumb machine. For example, it thinks that a return of 7 is preferable to a return of 6.5.  The reality is that we don’t know true returns; we are just forecasting them and there is significant uncertainty in our forecast. The difference between a return of 7 and 6.5 may be almost non-existent because we are essentially guessing about the future, whereas the optimizer assumes that 7 is better and loads up on that security[1].

Similarly, we estimate correlation between assets A and B to be .4 and correlation between A and C to be .45. If you already hold A in a portfolio and all else is equal, the optimizer will tend to add B and not C, because it sees a lower correlation. But correlations are notoriously unstable. When a crisis hits, your .4 and .45 go closer to 1, even though the difference between 4. and .45 was contrived. So the optimizer was really maximizing the error in your initial estimate.

Optimizers can be precisely wrong as opposed to broadly right. The ones used by large institutions today correct for many of these error maximization problems with sophisticated techniques such as resampling, robust optimization and, cone algorithms. And even with all the safeguards, the sophisticated institutional optimizers still run only under close supervision of experienced analysts.

The first generation of robo advisors is not using these sophisticated technologies, but rather the techniques that were used before the 2008 crisis. Letting machines that are essentially error maximizers automatically build investment portfolios is not a great idea – in fact it’s a terrible idea for your clients. Just because it can be done, doesn’t mean it should be.

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[1] Many robos use a technique called Black-Litterman to infer expected returns for assets. With this technique, instead of guessing returns ourselves, we use the current state of the market to infer future returns. Here we are basically assuming that the market is ‘smart’ and efficient and it knows the future return based on the way it prices the assets relative to one another today. Of course, trusting in market equilibrium this way does not improve precision; we still do not know the future and neither does Mr. Market. It regularly ‘decides’ to move from one equilibrium to another, thus changing all our implied estimates of the future.


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